Various systems have heretofore been proposed to isolate a mechanical payload, such as a platform for a sighting device, a camera, a gun, or the like from both low frequency movement or higher frequency vibrations of the supporting structure for the platform, for example, as where the platform is mounted on a moving vehicle, such as a dolly, an automobile, an airplane, or the like. Such stabilization systems must operate over a wide frequency range. One such platform stabilization system is described, for example, in U.S. Pat. No. 4,033,541 issued July 5, 1977, to the same inventor as the present application. In the stabilization system shown in the patent, a compliant isolator and a spherical bearing assembly are connected in series between the platform payload and the vehicle. Corrective torques are applied to the payload by linear actuators connected between the supporting structure of the vehicle and the payload. This system described in the patent works well over a broad range of frequencies and combinations of angular and translational vibratory inputs. However, the actuators may be required to accommodate relatively large translational displacements between the supporting base and the platform payload due to the translational displacements occurring primarily in the isolator. The isolator usually comprises springs or other compliant means which may have to be relatively "soft" to be effective at very low frequencies. For example, if the stable platform were used to mount a gun or artillery piece having a large recoil, relatively large displacements of the isolator might be encountered. The arrangement shown in the patent therefore might require actuators which have a substantial length of stroke. A disadvantage of the system shown in the patent, therefore, is the degree of motion required in the actuator to allow for translational as well as rotational displacement of the payload relative to the supporting base. The result is the magnetic actuators must be made with greater stroke length in the solenoid actuators or greater air gaps if linear motors are used as the actuators. The greater the air gaps or the longer the stroke of the solenoid, the greater the power and weight in the actuator needed to develop a given amount of torque.